Related papers: Diffusive solver: a diffusion-equations solver bas…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
It is shown that stochastic processes of diffusion type possess, in all generality, a structure of uncertainty relations and of coherent and squeezed states. This fact is used to obtain, via Nelson stochastic formulation of quantum…
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Harnessing spins as carriers for information has emerged as an elegant extension to the transport of electrical charges. The coherence of such spin transport in spintronic circuits is determined by the lifetime of spin excitations and by…
The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq…
By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on…
Equation for anomalous diffusion in momentum space, recently obtained in the recent paper (S.A. Trigger, ArXiv 0907.2793 v1, [cond-matt. stat.-mech.], 16 July 2009) is solved for the stationary and non-stationary cases on basis of the…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
Global solutions to the compressible Euler equations with heat transport by convection in the whole space are shown to exist through perturbations of Dyson's isothermal affine solutions. This setting presents new difficulties because of the…
A steady self-diffusion process in a gas of hard spheres at equilibrium is analyzed. The system exhibits a constant gradient of labeled particles. Neither the concentration of these particles nor its gradient are assumed to be small. It is…
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
A unified theoretical description of ballistic and diffusive carrier transport in parallel-plane semiconductor structures is developed within the semiclassical model. The approach is based on the introduction of a thermo-ballistic current…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
We propose a semi-classical model for femtosecond-laser induced demagnetization due to spin-polarized excited electron diffusion in the super-diffusive regime. Our approach treats the finite elapsed time and transport in space between…
A granular gas composed of inelastic hard spheres or disks in the homogeneous cooling state is considered. Some of the particles are labeled and their number density exhibits a time-independent linear profile along a given direction. As a…
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence…
In Clearing Up Mysteries -- The Original Goal (Maximum Entropy and Bayesian Methods: Cambridge, England, 1988 Springer, pp. 1-27) Jaynes derived Fick's Law for a dilute binary solution from Bayes' Theorem by considering, probabilistically,…
We introduce and study a family of cooperative exclusion processes whose microscopic dynamics is governed by selective kinetic constraints. They display, in sharp contrast to the simple symmetric exclusion process, density profiles that can…